Controlled reattachment in separated flows: a variational approach to recirculation length reduction

TL;DR

This paper develops a variational sensitivity analysis method to identify control strategies that effectively reduce recirculation length in separated flows, validated through nonlinear simulations and stability analysis.

Contribution

It introduces a variational approach to analytically determine flow control strategies for recirculation length reduction in separated flows.

Findings

Control strategies based on sensitivity analysis effectively reduce recirculation length.

Small cylinders and wall suction are identified as effective control devices.

Control reduces vortex shedding stability at moderate Reynolds numbers.

Abstract

A variational technique is used to derive analytical expressions for the sensitivity of recirculation length to steady forcing in separated flows. Linear sensitivity analysis is applied to the two-dimensional steady flow past a circular cylinder for Reynolds numbers $40 \leq Re \leq 120$, both in the subcritical and supercritical regimes. Regions which are the most sensitive to volume forcing and wall blowing/suction are identified. Control configurations which reduce the recirculation length are designed based on the sensitivity information, in particular small cylinders used as control devices in the wake of the main cylinder, and fluid suction at the cylinder wall. Validation against full non-linear Navier-Stokes calculations shows excellent agreement for small-amplitude control. The linear stability properties of the controlled flow are systematically investigated. At moderate Reynolds numbers, we observe that regions where control reduces the recirculation length correspond to regions where it has a stabilising effect on the most unstable global mode associated to vortex shedding, while this property does not hold any more at larger Reynolds numbers.